Modeling Longitudinal Data with Application to Educational and Psychological Measurement

Abstract

I review a class of models for longitudinal data, showing how it may be applied in a meaningful way for the analysis of data collected by the administration of a series of items finalized to the educational or psychological measurement. In this class of models, the unobserved individual characteristics of interest are represented by a sequence of discrete latent variables, which follows a Markov chain. Inferential problems involved in the application of these models are discussed considering, in particular, maximum likelihood estimation based on the Expectation-Maximization algorithm, model selection, and hypothesis testing. Most of these problems are common to hidden Markov models for time-series data. The approach is illustrated by different applications in education and psychology.

Keywords: backward and forward recursions, Expectation-Maximization algorithm, hidden Markov models, latent Markov models, Rasch model